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September 2010 Continuous isomorphisms from R onto a complete abelian group
Douglas Bridges, Matthew Hendtlass
J. Symbolic Logic 75(3): 930-944 (September 2010). DOI: 10.2178/jsl/1278682208

Abstract

This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of R onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if G is a complete (metric) abelian group that is the range of a continuous isomorphism from R, then G is noncompact. A special case occurs when G satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective mappings are proved en route to the main theorem. A Brouwerian example shows that some of our results are the best possible in a constructive framework.

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Douglas Bridges. Matthew Hendtlass. "Continuous isomorphisms from R onto a complete abelian group." J. Symbolic Logic 75 (3) 930 - 944, September 2010. https://doi.org/10.2178/jsl/1278682208

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1209.03047
MathSciNet: MR2723775
Digital Object Identifier: 10.2178/jsl/1278682208

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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